Stimulated Cherenkov radiation of a relativistic electron beam moving over a periodically corrugated surface (quasi-optical theory)

The propagation of waves over periodically corrugated surfaces and their excitation by relativistic electron beams are investigated within the framework of a quasi-optical approach. The dispersion equation is derived for normal waves under the assumption of a small (in the scale of the period and wavelength) corrugation depth, based on which two limiting cases are identified. In the first limiting case, the wave frequency is far from the Bragg resonance, and the propagation of waves can be described in terms of the impedance approximation, in which the fundamental spatial harmonic slows down. In the second limiting case realized at frequencies close to the Bragg resonance, the field is represented as two counterpropagating quasi-optical wave beams coupled on a corrugated surface and forming a normal surface wave. When interacting with an electron beam, convective instability, which can be used to realize amplifier regimes, corresponds to the first case, and absolute one, which is applied in surface-wave oscillators, corresponds to the second case. The developed theory is used to determine basic characteristics of amplifier and oscillator schemes: the growth rates, the energy exchange efficiency, and the formation of a self-consistent spatial structure of the radiated field. The practical realization of relativistic submillimeter amplifiers and surface-wave oscillators is shown to hold promise.